Number of significant figures

Exact numbers, such as the stoichiometric coefficients in a chemical formula or reaction, and unit conversion factors, have an infinite number of significant figures. A mole of CaCb, for example, contains exactly two moles of chloride and one mole of calcium. In the equality... 

Round each of the following to the stated number of significant figures. 

Report results for the following calculations to the correct number of significant figures. 

Calculate the molar concentration of NaCl, to the correct number of significant figures, if 1.917 g of NaCl is placed in a beaker and dissolved in 50 mF of water measured with a graduated cylinder. This solution is quantitatively transferred to a 250-mF volumetric flask and diluted to volume. Calculate the concentration of this second solution to the correct number of significant figures. 

Be careful to use the necessary number of significant figures for the molar masses.) For... 

Note that the values given for Wq limit the number of significant figures to four for H2 and to three for F2 and I2. 

Much of the additional material is taken up by what 1 have called Worked examples . These are sample problems, which are mostly calculations, with answers given in some detail. There are seventeen of them scattered throughout the book in positions in the text appropriate to the theory which is required. 1 believe that these will be very useful in demonstrating to the reader how problems should be tackled. In the calculations, 1 have paid particular attention to the number of significant figures retained and to the correct use of units. 1 have stressed the importance of putting in the units in a calculation. In a typical example, for the calculation of the rotational constant B for a diatomic molecule from the equation... 

In each example, the initial values of the factors are expressed in U.S. customary units, and the dimensionless value is calculated. Then the factors are converted to SI units, and the dimensionless value is recalculated. The two dimensionless values will be approximately the same. (Small variations occur due to the number of significant figures carried in the solution.)... 

Significant figures provide an indication of the precision with which a quantity is measured or known. The last digit represents, in a quantitative sense, some degree of doubt. For example, a measurement of 8.12 inches implies tliat Uie actual quantity is somewhere between 8.315 and 8.325 inches. This applies to calculated and measured quantihes quantities tliat are known exactly (e.g., pure integers) have an infinite number of significant figures. 

Frequently we need to know the number of significant figures in a measurement reported by someone else (Example 1.2). 

The number of significant figures is the number of digits shown when a quantity is expressed in exponential notation. 

Most measured quantities are not end results in themselves. Instead, they are used to calculate other quantities, often by multiplication or division. The precision of any such derived result is limited by that of the measurements on which it is based. When measured quantities are multiplied or divided, the number of significant figures in the result is the same as that in the quantity with the smallest number of significant figures. 

Count the number of significant figures in the numerator and in the denominator the smaller of these two numbers is the number of significant figures in the quotient... 

The numbers 1.8 and 32 are exact Hence they do not limit the number of significant figures in a temperature conversion that limit is determined only by the precision of the thermometer used to measure temperature. 

A number that is spelled out (one, two,...) does not affect the number of significant figures. 

Determine the number of significant figures in a measured quantity. 

Round off the following quantities to the indicated number of significant figures. 

Physical properties are those that do not involve changing the identity of a substance. Chemical properties are those that involve changing the identity of a substance. Extensive properties depend on the mass of the sample intensive properties do not. The precision of a measurement controls the number of significant figures that are justified by the procedure the accuracy of a measurement is its closeness to the true value. 

The abbreviation sf denotes the number of significant figures in the data. The frequencies, wavelengths, and energies are typical values they should not be regarded as precise. 

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